Galen R. Shorack

Bootstrapping robust regression

The bootstrap principle is justified for. robust M-estimates in regression, (A short proof justifying bootstrapping the empirical process is also given.)

Strong limit theorems for oscillation moduli of the uniform empirical process

SummaryLet % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Gqpe0-% rq0dXdd9vqaq-JfrVkFHe9pgea0dXdar-Jb9hs0dXdbPYxe9vr0-vr% 0-vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaiaadwfadaWgaa% WcbaGaamOBaaqabaGccaGGOaGaamiDaiaacMcaieaacaWFGaGaa8xp% aiaa-bcaieGacaGFUbWaaWbaaSqabeaadaWcbaadbaGaaGymaaqaai% aaikdaaaaaaOGaa8hiaiaa-HcaiiGacqqFtoWrdaWgaaWcbaGaa4NB% aaqabaGccaGGOaGaamiDaiaacMcacqGHsislcaWG0bGaaiykaiaacY% cacaWFGaGaa8hmamrr1ngBPrwtHrhAYaqeguuDJXwAKbstHrhAGq1D% VbacfaGaeWNzIyOaa8hiaiaa+rhacaGFGaGaeWNzIyOaeWhiaaIaaG% ymaaaa!5A33!

The Best Test of Exponentiality Against Gamma Alternatives

U_n (t) = n^{\tfrac{1}{2}} (\Gamma _n (t) - t), 0 \leqq t \leqq 1

Necessary and sufficient conditions for asymptotic normality of trimmed L-statistics

, denote the uniform empirical process based on the first n of a sequence ξ1, ξ2, ... of iid uniform (0,1) random variables where % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Gqpe0-% rq0dXdd9vqaq-JfrVkFHe9pgea0dXdar-Jb9hs0dXdbPYxe9vr0-vr% 0-vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaGGaciab-n5ahn% aaBaaaleaaieGacaGFUbaabeaakiaacIcacaWG0bGaaiykaGqaaiaa% 9bcacaqF9aGaa0hiaiaa+5gadaahaaWcbeqaaeXafv3ySLgzGmvETj% 2BSbacfaGaeWNeI0Iaa0xmaaaakiaa9bcadaaeWbqaaiaa9fdadaWg% aaWcbaGaa03waiaa9bdacaqFSaGaa4hDaiaa91faaeqaaaqaaiaa+L% gacaGF9aGaa0xmaaqaaiaa+5gaa0GaeyyeIuoakiaacIcacqaH+oaE% daWgaaWcbaGaamyAaaqabaGccaGGPaaaaa!53D6!

Uniform CLT, WLLN, LIL and bootstrapping in a data analytic approach to trimmed L-statistics

\Gamma _n (t) = n^{ - 1} \sum\limits_{i = 1}^n {1_{[0,t]} } (\xi _i )

Inequalities for quantile functions with a uniform studentized CLT that includes trimming

is the empirical distribution function. The oscillation modulus of Un is defined by % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Gqpe0-% rq0dXdd9vqaq-JfrVkFHe9pgea0dXdar-Jb9hs0dXdbPYxe9vr0-vr% 0-vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaiabeM8a3naaBa% aaleaacaWGUbaabeaakiaacIcacaWGHbGaaiykaGqaaiaa-bcacaWF% 9aGaa8hiaiaa-nhacaWF1bGaa8hCaiaa-bcacaWF7bGaa8hFaGqaci% aa+vfadaWgaaWcbaGaa4NBaaqabaGccaGGOaGaamiDaiabgUcaRiaa% dIgacaGGPaGaa8hiaeXafv3ySLgzGmvETj2BSbacfaGae0NeI0Iaa8% hiaiaa+vfadaWgaaWcbaGaa4NBaaqabaGccaGGOaGaamiDaiaacMca% caGG8bGaaiOoaiaa-bcacaWFWaWefv3ySLgznfgDOjdaryqr1ngBPr% ginfgDObcv39gaiyaacqaFMjIHcaGF0bGaeWNzIyOaeWha3hJaa8xm% aiaa-bcacqqFsislcqqFGaaicaGFObGaa4hlaiaa+bcacaGFObGaeW% NzIyOaeWha3hMaamyyaiaac2haaaa!720A!